Mechanical Properties

Mechanical Properties Mechanical Properties: (Forces ~ deformation) Strength ➼ Ductility ➼ Impact Creep ➼ Fatigue ➼ Wear 1

Definition of Stress: Tensile stress:

F σ = A0

Where F: force, normal to the crosssectional area, A0: original crosssectional area 2

Shear Stress Fs τ= A0

Fs: force, parallel to the crosssectional area A0: the cross-sectional area unit of stress:

Force N = 2 area m

1Pa = 1 Nm-2 ; 1MPa = 106Pa; 1GPa=109Pa 3

Some examples of stress: ✔ Simple tension: σ

(+) ✔ Simple compression: σ (-) ✔ Biaxial tension: σ ✔ Hydrostatic pressure: p ✔ Pure shear stress: τ

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Definition of strain Nominal tensile strain (Axial strain) l − l0 ∆l ε= = l0 l0

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Engineering shear strain γ = tan θ

For small strain: γ ≅θ

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Dilatation (Volume strain) Under pressure: the volume will change ∆V ∆= V

p p

p V-∆ V

p

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Hooke’s Law When strains are small, most of materials are linear elastic.

Young’s modulus σ

Tensile:

σ = Ε ε

Shear:

τ =Gγ

Shear modulus

Hydrostatic: – p = κ ∆

E ε

Bulk modulus 8

Elastic Behavior of materials

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Modulus of Elasticity - Metals

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Modulus of Elasticity - Ceramics

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Modulus of Elasticity - Polymers Polymers

Elastic Modulus (GPa)

Polyethylene (PE)

0.2-0.7

Polystyrene (PS)

3-3.4

Nylon

2-4

Polyesters

1-5

Rubbers

0.01-0.1 12

Example: NaCl By considering both attractive and repulsive force, α =0.58 Charge on electron q=1.602× 10-19 C Permittivity of vacuum: ε 0=8.854 × 10-12 Fm-1 r0≈ 2.5 × 10-10 m

0.58 × (1.602 × 10−19 ) 2 −1 S0 = = 8 . 54 Nm 4π × 8.854 × 10−12 × ( 2.5 × 10−10 )3 S0 8.54 E≈ = = 34.16GPa −10 r0 2.5 × 10

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Tension and Compression Test

Standard tensile specimen

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Tension and Compression Test

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Elastic Stress-Strain Curves

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Nonlinear Elastic σ -ε Curve

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Plastic Deformation

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Yielding and Yield Strength ✔ Yielding point: the turning point which separate

the elastic and plastic regions ✔ Yield strength: the stress at the yielding point. ✔ Offset yielding (proof stress): if it is difficult to determine the yielding point, then draw a parallel line starting from the 0.2% strain, the cross point between the parallel line and the σ −ε curve

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Tensile Strength

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Ductility

Measurement of ductility: Percent elongation Percent reduction in area

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Ductility – percent elongation  l f − l0   × 100 % EL =   l0 

Where lf: fracture length l0: the original gauge length

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Ductility – percent reduction in area  A0 − A f % RA =   A0

  ×100 

Where Af: cross-sectional area at the point of fracture A0: the original cross-sectional area 23

Typical mechanical properties for some metals and alloys

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Temperature influences on mechanical properties of Iron

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Resilience Resilience is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered. Modulus of resilience Ur εy

U r = ∫ σdε 0

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Modulus of Resilience

If it is in a linear elastic region,

1 1 σ y  σ y U r = σ yε y = σ y   = 2 2  E  2E

2

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Toughness Energy absorbed due to fracture – fracture toughness εf

U = ∫ σ dε 0

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True Stress and Strain ✔ True Stress

F σT = A

Where A is instantaneous cross-sectional area ✔ True Strain

l ε T = ln = ln(1 + ε ) l0 29

True Stress and Strain If no volume change during deformation: A0l0=Al Then

σ T = σ (1 + ε ) ε T = ln (1 + ε ) 30

True Stress-Strain Curve

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True Stress and Strain

σ T = Kε T

n

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Hardness F H= indented area

Hardness: a measure of a material’s resistance to localized plastic deformation

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Hardness

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Hardness Tests ✔ Simple and inexpensive ✔ Nondestructive ✔ Other mechanical properties often may be

estimated from hardness data, such as tensile strength

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Hardness Tests ✔ Rockwell Hardness Tests (HR): Diamond

cones or steel spheres ✔ Brinell Hardness Tests (HB): 10 mm sphere of steel or tungsten carbide ✔ Knoop Microhardness Tests (HK): Diamond pyramid ✔ Vickers Microhardness Tests (HV) 36

Hardness Tests

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Rockwell Hardness Tests

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Correlation between Hardness and Tensile Strength TS (MPa) = 3.45HB TS (psi) = 500HB

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3-point Bending tests

σ fs = σ fs =

3F f L 2bd Ff L

πR

2

3

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Stress-Strain Behavior of Ceramics – Flexure Tests

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Stress-Strain Behavior of Polymers

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Temperature influence

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Macroscopic Deformation

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